Solve (3z^5+7z^2)^2

$$( 3 z ^ { 5 } + 7 z ^ { 2 } ) ^ { 2 }$$

Evaluate

$$z^{4}\left(3z^{3}+7\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3z^{5}+7z^{2}\right)^{2}.

$$9\left(z^{5}\right)^{2}+42z^{5}z^{2}+49\left(z^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$9z^{10}+42z^{5}z^{2}+49\left(z^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$9z^{10}+42z^{7}+49\left(z^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$9z^{10}+42z^{7}+49z^{4}$$

Expand

$$9z^{10}+42z^{7}+49z^{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3z^{5}+7z^{2}\right)^{2}.

$$9\left(z^{5}\right)^{2}+42z^{5}z^{2}+49\left(z^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$9z^{10}+42z^{5}z^{2}+49\left(z^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$9z^{10}+42z^{7}+49\left(z^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$9z^{10}+42z^{7}+49z^{4}$$